Let f ( x ) = 〚 cos x 〛 , − π ≤ x ≤ π . (a) Sketch the graph of f . (b) Evaluate each limit, if it exists. (i) lim x → 0 f ( x ) (ii) lim x → ( π / 2 ) − f ( x ) (iii) lim x → ( π / 2 ) + f ( x ) (iv) lim x → ( π / 2 ) f ( x ) (c) For what values of a does lim x →0 f ( x ) exist ?
Let f ( x ) = 〚 cos x 〛 , − π ≤ x ≤ π . (a) Sketch the graph of f . (b) Evaluate each limit, if it exists. (i) lim x → 0 f ( x ) (ii) lim x → ( π / 2 ) − f ( x ) (iii) lim x → ( π / 2 ) + f ( x ) (iv) lim x → ( π / 2 ) f ( x ) (c) For what values of a does lim x →0 f ( x ) exist ?
Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)
y
4
x
(a) lim f(x)
X→ 2-
(b)
lim f(x)
X→2+
(c) lim_f(x)
X→ 2
(d) f(2)
(e)
(f) f(4)
xlim f(x)
-4
-2
0
2
Use the given graph of f to state the value of each quantity, if it exists. (If an answer does not exist, enter DNE.)
(a) lim f(x)
x → 2-
(b) lim f(x)
x → 2+
(c) lim f(x)
X→ 2
(d) f(2)
(e)
COCO
lim f(x)
X→ 4
(f) f(4)
YA
-4
-2.
0
2
4 x
1. Consider the function f(r) = ( Ja- 1), where a > 0, x > 0.
(a) Tell if f is an indeterminate form? If yes, write its form, and if no, explain why.
(b) If 0< a < 1, show that lim. f(x) is a negative number.
Chapter 2 Solutions
James Stewart Calculus for MAT 127/128/229 8th edition
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